Question

1. identify whether the data is classified as categorical or quantitative.

c q eye color
c q temperature
c q mass of various objects

1. use the raw data shown to find the measures of central tendency and measures of variation.

11 5 5 3 7 5
find the following:
mean: median:
mode: midrange:
range: what is the deviation for the value of 11?

Explanation:

Step1: Sort the data

Sort the data set \(3,5,5,5,7,11\)

Step2: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 6\) and \(\sum_{i=1}^{6}x_{i}=3 + 5+5+5+7+11=36\). So \(\bar{x}=\frac{36}{6}=6\)

Step3: Calculate the median

Since \(n = 6\) (even), the median \(M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}\). Here \(x_{3}=5\) and \(x_{4}=5\), so \(M=\frac{5 + 5}{2}=5\)

Step4: Calculate the mode

The mode is the most - frequently occurring value. The value \(5\) occurs \(3\) times, so the mode is \(5\)

Step5: Calculate the midrange

The midrange \(MR=\frac{\text{Min}+\text{Max}}{2}\), where \(\text{Min}=3\) and \(\text{Max}=11\). So \(MR=\frac{3 + 11}{2}=7\)

Step6: Calculate the range

The range \(R=\text{Max}-\text{Min}\), so \(R=11 - 3=8\)

Step7: Calculate the deviation for the value of \(11\)

The deviation \(d=x-\bar{x}\). For \(x = 11\), \(d=11-6 = 5\)

Answer:

Mean: \(6\)
Median: \(5\)
Mode: \(5\)
Midrange: \(7\)
Range: \(8\)
Deviation for \(11\): \(5\)